If tanθ = 3 over 10 then find the value of (1+sinθ)(1-sinθ) over (1+cosθ)(1-cosθ).

If tanθ = 3 over 10 then find the value of…

If $tan\theta = {{3} \over 10}$ then find the value of ${{(1+sin\theta)(1-sin\theta)} \over (1+cos\theta)(1-cos\theta)}.$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. ${{100} \over 9}$ .

Given that

$tan\theta = {{3} \over 10}$

Formula used

sin²θ + cos²θ = 1

Therefore,

${{(1+sin\theta)(1-sin\theta)} \over (1+cos\theta)(1-cos\theta)}$ = 1 - sin²θ / 1 - cos²θ

⇒ cos²θ / sin²θ

⇒ cot²θ

Since tanθ = $\frac{3}{10}$ , cotθ = $\frac{10}{3}$

Hence, cot²θ = $\frac{100}{9}$ .